Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems

The Asymptotic Performance of Linear Echo State Neural Networks

In this article, a study of the mean-square error (MSE) performance of linear echo-state neural networks is performed, both for training and testing tasks. Considering the realistic setting of noise present at the network nodes, we derive deterministic equivalents for the aforementioned MSE in the limit where the number of input data $T$ and network size $n$ both grow large. Specializing then the network connectivity matrix to specific random settings, we further obtain simple formulas that provide new insights on the performance of such networks

Whole brain functional connectivity using phase locking measures of resting state magnetoencephalography

The analysis of spontaneous functional connectivity (sFC) reveals the statistical connections between regions of the brain consistent with underlying functional communication networks within the brain. In this work, we describe the implementation of a complete all-to-all network analysis of resting state neuronal activity from magnetoencephalography (MEG). Using graph theory to define networks at the dipole level, we established functionally defined regions by k-means clustering cortical surface locations using Eigenvector centrality (EVC) scores from the all-to-all adjacency model. Permutation testing was used to estimate regions with statistically significant connections compared to empty room data, which adjusts for spatial dependencies introduced by the MEG inverse problem. In order to test this model, we performed a series of numerical simulations investigating the effects of the MEG reconstruction on connectivity estimates. We subsequently applied the approach to subject data to investigate the effectiveness of our method in obtaining whole brain networks. Our findings indicated that our model provides statistically robust estimates of functional region networks. Application of our phase locking network methodology to real data produced networks with similar connectivity to previously published findings, specifically, we found connections between contralateral areas of the arcuate fasciculus that have been previously investigated. The use of data-driven methods for neuroscientific investigations provides a new tool for researchers in identifying and characterizing whole brain functional connectivity networks. © 2014 Schmidt, Ghuman and Huppert

The Role of Landscape Connectivity in Planning and Implementing Conservation and Restoration Priorities. Issues in Ecology

Landscape connectivity, the extent to which a landscape facilitates the movements of organisms and their genes, faces critical threats from both fragmentation and habitat loss. Many conservation efforts focus on protecting and enhancing connectivity to offset the impacts of habitat loss and fragmentation on biodiversity conservation, and to increase the resilience of reserve networks to potential threats associated with climate change. Loss of connectivity can reduce the size and quality of available habitat, impede and disrupt movement (including dispersal) to new habitats, and affect seasonal migration patterns. These changes can lead, in turn, to detrimental effects for populations and species, including decreased carrying capacity, population declines, loss of genetic variation, and ultimately species extinction. Measuring and mapping connectivity is facilitated by a growing number of quantitative approaches that can integrate large amounts of information about organisms’ life histories, habitat quality, and other features essential to evaluating connectivity for a given population or species. However, identifying effective approaches for maintaining and restoring connectivity poses several challenges, and our understanding of how connectivity should be designed to mitigate the impacts of climate change is, as yet, in its infancy. Scientists and managers must confront and overcome several challenges inherent in evaluating and planning for connectivity, including: •characterizing the biology of focal species; •understanding the strengths and the limitations of the models used to evaluate connectivity; •considering spatial and temporal extent in connectivity planning; •using caution in extrapolating results outside of observed conditions; •considering non-linear relationships that can complicate assumed or expected ecological responses; •accounting and planning for anthropogenic change in the landscape; •using well-defined goals and objectives to drive the selection of methods used for evaluating and planning for connectivity; •and communicating to the general public in clear and meaningful language the importance of connectivity to improve awareness and strengthen policies for ensuring conservation. Several aspects of connectivity science deserve additional attention in order to improve the effectiveness of design and implementation. Research on species persistence, behavioral ecology, and community structure is needed to reduce the uncertainty associated with connectivity models. Evaluating and testing connectivity responses to climate change will be critical to achieving conservation goals in the face of the rapid changes that will confront many communities and ecosystems. All of these potential areas of advancement will fall short of conservation goals if we do not effectively incorporate human activities into connectivity planning. While this Issue identifies substantial uncertainties in mapping connectivity and evaluating resilience to climate change, it is also clear that integrating human and natural landscape conservation planning to enhance habitat connectivity is essential for biodiversity conservation

Functional reorganisation and recovery following cortical lesions: A preliminary study in macaque monkeys.

Damage following traumatic brain injury or stroke can often extend beyond the boundaries of the initial insult and can lead to maladaptive cortical reorganisation. On the other hand, beneficial cortical reorganisation leading to recovery of function can also occur. We used resting state FMRI to investigate how cortical networks in the macaque brain change across time in response to lesions to the prefrontal cortex, and how this reorganisation correlated with changes in behavioural performance in cognitive tasks. After prelesion testing and scanning, two monkeys received a lesion to regions surrounding the left principal sulcus followed by periodic testing and scanning. Later, the animals received another lesion to the opposite hemisphere and additional testing and scanning. Following the first lesion, we observed both a behavioural impairment and decrease in functional connectivity, predominantly in frontal-frontal networks. Approximately 8 weeks later, performance and connectivity patterns both improved. Following the second lesion, we observed a further behavioural deficit and decrease in connectivity that showed little recovery. We discuss how different mechanisms including alternate behavioural strategies and reorganisation of specific prefrontal networks may have led to improvements in behaviour. Further work will be needed to confirm these mechanisms.This work was supported by the MRC intramural program MC-A060-5PQ10 (MA, DM, JD, AB), an MRC Career Development Award G0800329 (AM)